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Circle Theorems-“No Brainers”

1. Central Angle. Circle Theorems-“No Brainers”. Equals the arc. 2. Inscribed Angle. Equals ½ the arc. 3. Diameter ┴ Chord. BISECTED chords & arcs Right <‘s formed. 4. Angles formed by 2 chords. 5. Segments formed by 2 chords. POP = POP. (CE)(ED)=(AE)(BE).

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Circle Theorems-“No Brainers”

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  1. 1. Central Angle Circle Theorems-“No Brainers” Equals the arc 2. Inscribed Angle Equals ½ the arc 3. Diameter ┴ Chord BISECTED chords & arcs Right <‘s formed

  2. 4. Angles formed by 2 chords 5. Segments formed by 2 chords POP = POP (CE)(ED)=(AE)(BE) 6. Angle formed by Chord and Tangent Equals ½ the arc

  3. W O O W 7. Angle formed by 2 secants 8. Segments formed by 2 secants WO = WO (whole)(outter)

  4. T² O W 9. Angle formed by a tangent & a secant 10. Segments formed by a tangent & a secant T² = WO Tangent² =(whole)(outter)

  5. 11. Radius and Tangent Perpendicular… right <‘s are formed 12. Angle formed by 2 tangents (360-x) x 13. Segments formed by 2 tangents Are equal… ”Clown Hat” Theorem

  6. d r r congruent • Congruent chords have _____________ arcs. • A circle has _________ degrees. • Parallel lines intercept _____________ arcs. • 17. A diameter creates 2 arcs of _________. 360º congruent 180º 180º 2 18. A diameter = ___ radius 180º

  7. Circle Theorems used in Proofs • All diameters or radii of a circle are congruent. • Congruent chords intercept congruent arcs. • Congruent arcs are intercepted by congruent chords. • Parallel chords intercept congruent arcs. • A tangent is perpendicular to a radius at the point of tangency. • Tangents drawn to a circle from the same exterior point are congruent. • Congruent central angles intercept congruent arcs. • Congruent arcs are intercepted by congruent central angles. • 7. Angles inscribed to the SAME arc are congruent. • 8. Angles inscribed to CONGRUENT arcs are congruent. • 9. An angle inscribed in a semi-circle is a right angle. • 10. A triangle inscribed in a semi-circle is a right triangle. • Two circles with congruent radii or congruent diameters are congruent.

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